On Lie's classification of nonsolvable subalgebras of vector fields on the plane
Published: Jul 30, 2025
Last Updated: Jul 30, 2025
Authors:Hassan Azad, Indranil Biswas, Ahsan Fazil, Fazal M. Mahomed
Abstract
A brief proof of Lie's classification of finite dimensional subalgebras of vector fields on the complex plane that have a proper Levi decomposition is given. The proof uses basic representation theory of sl(2, C). This, combined with \cite{ABF2} and \cite{ABF3} completes the classification of finite dimensional subalgebras of vector fields on the complex plane.